Method and apparatus for propagating traveling wave energy through resonant matter

ABSTRACT

Coherent light or other coherent traveling wave energy is passed through a resonant medium containing matter normally resonant to the energy and opaque. The light pulse energy satisfies an area condition, pi + Delta , and a duration condition less than the relaxation time of the matter of which the resonant medium is composed. In passing through the matter, the pulse is reshaped and delayed. Embodiments of the invention include pulse shapers, delay lines, storage elements and logic elements. The frequency characteristics of the input pulse are also changed leading to embodiments of the invention useful as filters and frequency modulators. These properties result from the details of the resonance bands of the matter of which the medium is composed and, accordingly, lead to an extension of the invention useful in the identification of materials and the analysis and measurement of their properties and structure.

United States Patent [1 1 Hahn et al. 1 Jan. 30, 1973 54 METHOD ANDAPPARATUS FOR 2,92l,l84 1/1960 Fruengel 250/199 PROPAGATING TRAVELING wv 3,200,354 8/l965 White ..330/s.5 3.293.438 l2/l966 Davis, Jr ..2SO/l99MATTER Primary Examiner-Albert .l. Mayer [75] Inventors: Erwin L.Hahn,Berkeley;Samuel L. Atmrney-Flehr, Hohbach, Test, Albritton and Her-McCall, Albany, both of Calif. bert [73] Assignee: 'gleifoill-zgsnts ofthe University of 57] ABSTRACT Coherent light or other coherenttraveling wave ener- [22] July gy is passed through a resonant mediumcontaining [2i] Appl. No.: 64,022 matter normally resonant to the energyand Opaque. The light pulse energy satisfies an area condition, 11Related Application Data A, and a duration condition less than therelaxation [63] Continuation of N0 635 193 May 1 1967 time of the matterof which the resonant medium is abandoned composed. in passing throughthe matter, the pulse is reshaped and delayed. Embodiments of theinvention [52] "250/199 331/945 307/311 include pulse shapers, delaylines, storage elements 350/266 324/8] 324/96: and logic elements. Thefrequency characteristics 'of [51] Int Cl ..H04b 9/00 the input pulseare also changed leading to embodi- [58] Field 3 4 ments of theinvention useful as filters and frequency 3 3 H 5 56 modulators. Theseproperties result from the details of 96 333/20 the resonance bands ofthe matter of which the medium is composed and, accordingly, lead to anextension [56] References Cited of the invention useful in theidentification of materials and the analysis and measurement of theirproper- UNITED STATES PATENTS ties and structure- 2,623,l65 12/1952Mueller et al. ..250/l99 28 Claims, 23 Drawing Figures PROGRAWER 0 AND CMPUTER lro PATENTEDJAN30 1975 3,714,438

sum 1 or 6 INVENTOR.

Erwin L. Hahn By Samuel L. McCall 7fl-Kh, ("1- 7:4

Attorneys PAIENTEDJMSO I975 3, 714,438

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INVENTOR. Erwin L. Hahn BY Samuel L. McCall Attorneys IATENTEDJ/m 30I975 3. 714.438 SHEET 6 OF 6 Fig. /8A Fig. I88 Fig. /9

PROGRAMMER AND COMPUTER \[70 I69 '3" Qi I60 I63 I65 I57 F i g. 20

INVENTOR Erwin L. Hahn BY Samuel L. McCall 7 414 Jaz- W Attorneys METHODAND APPARATUS FOR PROPAGATING TRAVELING WAVE ENERGY THROUGH RESONANTMATTER This application is a continuation of application Ser. No.635,193, filed May 1,1967, now abandoned.

The invention described herein was made in the course of or under agrant from the National Science Foundation, an agency of the U.S.Government.

BACKGROUND AND SUMMARY OF THE INVENTION This invention relates to thepassage of traveling wave energy through matter which is resonantthereto. More particularly, the invention relates to the passage ofelectromagnetic energy, such as light, through such resonant matter.

Heretofore, matter resonant to a particular form and frequency oftraveling wave en rgy, such as light, absorbs such energy and isaccordingly considered opaque. In general, it is an object of thepresent invention to provide a method for propagating traveling waveenergy, such as light, through such matter.

This invention is predicated on the discovery that a coherent travelingwave pulse satisfying certain criteria as to pulse strength and durationwill pass through matter which would normally absorb it. For example, alaser pulse satisfying such criteria has been propagated through anormally opaque, homogeneous crystal of ruby.

As the pulse propagates through the medium it is changed in intensity,shape, polarization, frequency characteristics, direction ofpropagation, phase, and convergence or divergence. Also, the pulse isdelayed and its frequency make-up can be changed. Some input pulses arebroken down into a sequence of smaller output pulses spaced in time, thenumber of which depends upon the strength and duration of the inputpulse. The above effects depend upon the nature of the matter of whichthe medium is constructed and serve to provide information concerningits structure.

In the discussion herein the expression pulse will be used in connectionwith identifying the input signal, the output signal and the detectedoutput pulse, i.e., the envelope of the output signal. With respect tothe input signal the output signal, pulse will refer to a burst ofperiodically varying traveling wave energy. It is believed that theaforementioned usage will not cause confusion since the context willmake the particular meaning clear.

Among the other objects of the invention are the following: to transmitcoherent pulses of electromagnetic radiation through media, at or nearresonance, where the media is ordinarily opaque to incoherent pulses ofelectromagnetic radiation at or near the same frequency; to providemethod and means for establishing the critical resonance thresholdeffect of traveling wave pulse or pulses, in time sequence, withinitially unexcited vibrators contained in media into which the pulsesare transmitted; to provide a means for monitoring the pulse or pulsesafter having traversed the media and to sense the intensity of saidpulses relative to the intensity of the input pulse or pulses; toprovide means and method for relating and correlating properties of timedelay, phase shift, frequency, pulse shape, pulse width, beam direction,birefringence effects, and plurality of pulses with respect to thesesame properties of the input pulse or pulses and the properties of theresonant medium through which the input pulses pass; to provide meansfor chemical and physical analysis of media containing constituentswhich are resonant to the incoming pulsed radiation, includingfrequencies as low as radiofrequency and extending through the opticalrange, which excite resonators of magnetic dipole orelectric dipole incharacter, or both; to measure the decay of pulses of coherent radiationabove the threshold condition as a function of target media or sampleconcentration of resonators, length of sample, or as a function of otherphysical conditions such as temperature, pressure, annealing (of solid),external electric and magnetic fields, in order to carry out chemicalqualitative and quantitative analysis; physical assessment of matterproperties, be the matter liquid, solid, or gas; to provide means formonitoring the delayed, coherent electromagnetic wave pulses in theresonant medium for purposes of digital memory storage and for theirrecirculation back into the input of the medium for computer purposes;to provide method and apparatus for delaying, shaping, and changing thefrequency spectrum of coherent traveling waves; to provide coherentpulse storage and logic method and apparatus.

These and other objects of the invention will become apparent from thefollowing description when taken in conjunction with the accompanyingdrawings.

DESCRIPTION OF THE DRAWINGS Referring to the drawings: H

FIG. 1 is a graph depicting branch-solutions to the equation coveringtraveling wave propagation through resonant medium in accordance withthe invention.

FIG. 2 is a plot of the electric field intensity versus distance (2)through the resonant medium and is a function of time for nonpropagatingconditions.

FIGS. 3A and 3B and 3C are plots of the electric field intensity versusdistance (2) through the resonant medium and time for variouspropagating conditions.

FIGS. 4 and 5 are graphs depicting the output pulse wave shape as afunction of the input wave pulse bandwidth versus the medium resonancebandwidth.

FIG. 6 is a diagrammatic view of apparatus by which the invention wasput into practice.

FIG. 7 is a set of energy level diagrams for the apparatus of FIG. 6.

FIG. 8 is a bar graph depicting the output energy of the apparatus ofFIG. 6 as a function of the energy of the input signal.

FIG. 9 is a diagrammatic view of a modified form of apparatusincorporating the invention and used for comparing the strength of theinput and output signals.

FIGS. 10A through 10C are oscillograph traces of the input and outputsignals obtained from operation of the apparatus of FIG. 9.

FIG. 11 is a diagrammatic view of a system for the transmission ofelectromagnetic wave pulse over long distances, constructed according tothe invention.

FIG. 12 is a schematic diagram of apparatus for adjustably delayingcoherent wave pulses constructed according to the invention.

FIG. 13 is a graph of the delay properties of the apparatus of FIG. 12when operated as a storage device.

FIG. 14 is a schematic diagram of another form apparatus for adjustablydelaying coherent wave pulses constructed in accordance with theinvention.

FIG. 15 is a diagrammatic view of delay and storage apparatusconstructed according to the invention and useful in computerapplications.

FIG. 16 is a diagrammatic view of apparatus performing logic constructedaccording to the invention.

FIG. 17 is a diagrammatic view of a modified embodiment of a delay linestructure for use in microwave region, constructed according to theinvention.

FIGS. 18A and 18B are graphs depicting the operation of the invention infiltering coherent traveling waves.

FIG. 19 is a graph depicting the operation of the invention in frequencyshifts coherent traveling waves.

FIG. 20 is a schematic drawing of apparatus for carrying out studies onthe properties of materials.

THEORETICAL DESCRIPTION In order to facilitate the explanation andunderstanding of the invention, there follows a brief simplifiedtreatment using an analogy to a mechanical system of pendulums. Afterthis, a more complete and rigorous treatment based upon electromagnetictheory and quantum mechanics is given.

The essence of the invention can be understood by reference to ananalogy which is not literally in correspondence in all respects withthe actual phenomenon of the critical pulse transmission effect, but ishelpful nevertheless. Consider first a ball of given mass M which isrolled with a certain initial velocity V along a grooved track. The ballhas a certain energy which we shall assume compares to the energy of agiven light pulse, for example. Let us consider next a sphere of likemass M suspended on one end of a rigid weightless rod, and the other endof the rod is fixed on a pivot above this mass, so that the combinationbehaves as a rigid pendulum. Let M be suspended in the path of therolling ball M, so that upon impact of M with M, the pendulum will swingin an arc which is planar with the trajectory of M on the track. Let thependulum with M represent a typical resonator in the aforementionedoptical medium, ready to be excited by the impinging light pulse,represented by the moving mass M. IfM has a velocity v (neglectingfriction) less than a critical velocity value v, M will strike M, and Mwill swing in an are out of the way of M after the impact. Mass M willcontinue forward in its rolling trajectory at a diminished v, v afterthe impact. Ifa succession of such pendulums are placed in the path ofM, the mass M will eventually come to rest, which is representative ofabsorption of the light pulse. The condition for pulse transmissionabove the critical threshold has its analogy in the condition that themass M now strikes M', now as a more powerful pulse, with a velocity v 2v,, so that the pendulum swings through an are just slightly greaterthan 180 or 1r radians. The model is designed so that at this critical1r condition, mass M comes completely to rest after the impact with M.All of the energy originally in M is now momentarily contained in M.However M of the pendulum swings down from its vertical position at 11through angle 0 greater than 180, and strikes M, giving it a renewedimpact momentum in the same forward direction at which M originallystruck M Mass M with its renewed energy and momentum can now repeat thisprocess with additional pendulums down along the line of its trajectory,and the mass M can pass through the resonating pendulums. The analogyshows how the pendulum absorbs energy from the ball at a first impact.But after the pendulum swings around beyond the critical 180, 11"condition, the ball recovers this energy (neglecting friction). Thependulum now emits the energy it previously absorbed, a take and giveprocess with respect to the ball M. The process with a light pulsetraversing a resonant medium is remarkably similar to the aboveanalogue, but of course the mechanical analogue does not describe allaspects of the effects resulting from the invention.

The above-mentioned critical absorption-emission transmission of a lightpulse is consistent and analogous to a precise prediction ofelectromagnetic theory when coupled to the quantum mechanical equationsof motion of the two level atomic system resonance to incoming light.When the pendulum is at rest, waiting for a collision, we mean that theatoms in a small portion of the medium, in the front entry face, let ussay, are in the optical, unexcited ground state. The collision occurswhen the light enters and excites the electrons from their ground towardexcited states. The electric field E in the traveling wave pulse mustact for a sufficient length of time 7 upon the electrons so that theyare excited completely from the ground state into the excited state. Thetransparency effect, however, will take over only if the opticalexcitation is sufficient to make the electrons overshoot, at leastinitially, so that they return, ever so slightly back toward the groundstate by an amount A radians. In this language of the optical pendulum,the electrons undergo a n+A excursion, if the initial pulse hassufficient area so that where K is a constant which is a measure of thedipole strength of the optical oscillator. For additional reference, thereader is referred to the following articles in which the terminologywhich exemplified origin and development of the area inangular terms;Spin Echoes by E. L. Hahn, Physical Review, Volume No. 4, pages 580 to598 dated Nov. 15, 1950, particularly page 583 and the associateddiscussion, and Pulse Techniques and Microwave Spectroscopy by R. H.Dicke and R. H. Romer, The Review ofScientific Instruments, Volume 26,No. 10, October, 1955, particularly pages 916 and 918.1f0 1r A, forexample, the transparency effect will not occur and the pulse will beabsorbed in the medium. We assume, of course, that no friction ispresent relating to random spontaneous emission or phonon relaxation dueto thermal vibrations. Even so, losses will occur because the atomsremain excited and capture the energy originally contained in the pulse.For the condition 0 1r A, the incoming pulse, of course, loses someenergy, proportional to J E dt.

But as it travels forward into the medium, the overall pulse areaincreases because the emission cycle of the optical excitation adds areato the lagging edge of the pulse, in spite of the pulse energy loss dueto absorption during the leading edge. Therefore the area 0- E dtincreases perrnissibly, even though fE dt decreases. As the pulsetraverses further into the medium the area 0 approaches the value 2 andthe energy loss fE dt approaches zero. Consequently, the pulse proceedsthereafter undamped and reshaped into a smooth symmetrical shape. FIG. 1in the enclosed technical description shows the behavior of the pulsearea dependence upon distance z and time t for cases 0 1r A 0.9 and0=1r+A= 1.1. The change in Oasafunction of distance 2 is given in FIGS.2 and 3A-C. If the pulse is not initially a 2 pulse, but is at leastgreater than 1r,the initial loss in energy from the pulse is notnecessarily severe, and a considerable portion of the pulse power maystill remain after the pulse has become stable.

In the following discussion electromagnetic theory and quantum mechanicsare taken into account. Let a pulse of coherent light having a duration,hereinafter termed pulse width 1,, impinge on a medium of opticallyresonant matter. For times 1-,, short compared to T the inverse of thehomogeneous broadening contribution to the optical line width 1/1", ofthe medium, the pulse propagates. The basic propagation effect is formedfrom the following analysis for a limiting case of a coherent planewave, taken to be circularly polarized so that:

length, and n is the constant refractive index of '45 the medium. E(z,t)is assumed slowly varying so that (SE/Sz) (E/ar) and (oE/St) wE. Let themedium include N solute ions per cm in the optical ground state andpresent a two level, inhomogeneously broadened symmetric spectraldistribution function g(Am) to the driving pulse; and the center of thespectrum is tuned to frequency co, with ions defined offresonance byamount Am. The condition (0" T Tp T, is assumed, where T,* g(()) is theinverse inhomogeneously broadened line width caused by a spread of localstatic crystalline fields, and HT: 1/ T l/TJ. In the language ofmagnetic resonance, the two level system can be represented by aneffective macroscopic electric dipole moment F= li u v v (XK/w) whereu,,, WKo, w are orthogonal unit vectors in the fictitious referenceframe rotating at frequency to about the direction. At a particular Am,F is described by the equation dT/dz =Fx 0,1 E+ (Ma 2 In the undampedBloch equation notation (F. Bloch, Phys. Rev. 70, 460 (1946) electricdipole absorption 6 v and dispersion (u) components combine with a thirdcomponent (K W/m) (in place of M;), where W is the ion energy spectraldensity per emf, k 2p/n, and p is the x or y component of the electricdipole moment of v the transition. In general, any combination of at and1r optical transitions may be handled by this model. For simplicity,there is considered here only the behavior of moment Finduced by onecircularly polarized component E (z,t). After any pulse, the vector Pwith Am 0 is turned through a net angle However, E (z,t) is determinedby its initial form at z 0, and by the superposition of all the dipolesources throughout the spectrum, as seen from the reduced Maxwellequation for the forward traveling wave: 01221, a +2 we, r

dO/dz 01/2 sin0, which has the solution n (z)/2)=(tan J P z/2)- (7 Eq.(5) follows from Eq. (7) in the limit of small 0. Here 0,, is therotation angle for those ions with An 0 at z 0, the entry face plane ofthe medium.

The branch solutions of 0 versus 1 from Eq. (7) are plotted in FIG. 1.For a given 0, the medium entry plane is assigned the corresponding 1which defines z 0 in Eq. (1). For the sample initially in the excitedstate, 0 evolves in the z direction. Units of z are in multiples of 1m".

Plots for E versus 2 and t are shown in FIGS. 2 and 3A for cases 0,,=0.9,. and 0o= 1.1.1,, with arbitrary pulse widths. Initial shapes arechosen to be Gaussian. The unit of time is conveniently chosen in termsof input pulse width -r,,. For fixed 0,, units of E are determined fromEq. (3 Units of z are in multiples of 1m".

For initial pulse areas 0,, 1r, below the critical area at 0,, 1r, thepulse area diminishes toward 0(z) 0 for increasing J JEJ jfqtflq 20-212519-. i.

Above the critical area, a 0 1.1,, pulse increases in area (0 (z) -fEdt)toward the iimit'z when db/'ii'z')='0. During this process the pulseloses some energy over a number of absorption lengths or and isreshaped. The 2,r pulse formed appears to be the traveling wave pulsegiven by E (z,t)=2/K1sech[l/r(tz/ 1, 8) and is unique in that itrepresents the only finite energy pulse solution to Eq. (4) which isunattenuated and retains its shape. The induced polarization radiates insuch a way as to produce the same field pulse given above. V is thepulse velocity, and r is the final pulse width. The final pulse energyin this undamped model is conserved because any optical ion, independentof its assigned Aw, is momentarily excited from its ground state to acoherent superposition of ground and excited states, and then isreturned completely to the ground state after the pulse has gone by.Pulse retardation or delay occurs because the pulse is depleted inenergy at its leading time edge during absorption, but the absorbedenergy is returned to the lagging edge during emission. Calculationsshow that a given arbitrary input pulse with 0,, 21m divides into nseparate 217 pulses of the shape given by Eq. (8), after traversing somedis ance into the medium.

The solution to the coupled Equations (2) and (4) for a pulse of theform (8) may be found without the assumption that T; r,. The componentsof Fare 2 Nice; 2

2 1+(Aw-r) with This solution would also apply to any magnetic momentM(Aw) in a magnetic resonance pulse experiment where the imposed rfcavity pulse field H (t) is of the form of Eq. (8).

The reciprocal pulse velocity is found to be n V E 10 which reduces to V(0: 1/2) for T 1 and err n/c. The special results (8), (9), and (10) arevalid for nonsymmetric g(Aw) ifk in Eq. (I) is replaced by Assumingphenomenological damping terms added to Eq. (2) in a manner followingBloch, (F. Bloch, Phys. Rev. 70, 460 (1946) we find for T 1- T T that)=(41r/3)NKwg( i) 3)), where T is the energy damping time constant, andthe pulse energy per cm is given by The constant loss rate isproportional to the product of the pulse delay time arr/2 per unitsample length and the fraction T,*/'r of the ions excited. The pulse isassumed to deviate only slightly from the forfn (8) for a plane wave,and diffraction effects are neglected. However, the dependence of k on1' (and therefore the pulse intensity) indicates the existence of aninstability effect similar to self-focusing for 0) applied to the highfrequency side of the resonance line. The reverse focusing tendencyshould occur on the low frequency side.

In actual practice, the medium presents optical resonances or opacity tolight in which the energy is irreversibly dissipated in the form ofthermal vibrations and spontaneous emission. One then asks whether themedium still permit coherent light pulses to pass through with lessattenuation than if the light were incoherent, i.e., from ordinary lampsources. The answer is that the medium will be more transparent to thelight the shorter the light pulse duration time (1,) is with respect tothe random damping relaxation time (T of the optical resonance; that is,the condition T,'? 1-,, should hold. If any opaque medium therefore isan impediment to ordinary incoherent light pulses, then coherent lightpulses should transmit energy, to some degree, through to the other sideof the medium boundary, depending upon how short the pulses are. Thedecay of such coherent pulse intensities will not be exponentiallydecreasing for T 1-,, but at a slower rate, reaching essentially a decayproportional to distance through the medium for T 7,, but T finite. Itmust be kept in mind that the resonance linewidth of the medium may bestatically broadened (inhomogeneous broadening) because ofa staticdistribution of two level resonance transitions, and still permit 7, tobe rather long. For example in free atoms T is typically 10'' seconds.However, present technology is capable, by mode locking lasertechniques, of producing coherent optical pulses as short as r, 10' to10- seconds in width. Therefore, the enhancement of transmission ofcoherent light pulse, or similar effects of other electromagnetic orphonon (sound wave) radiation, suggests the potentiality of applyingthis invention to communication by laser beams, for example, throughclouds and other opaque media, or through denser media which arereasonably homogeneous in character.

Even though the pulse should be shorter than the relaxation time of themedium, it is expected that a practical pulse duration for practicingthe invention would be preferably less about one-tenth of the relaxationtime of the media. Since gases at ambient temperature have relaxationtimes of the order of 10' 10' seconds and solids and liquids haverelaxation times of the order of 10' 10' seconds, it is seen that themode locked laser pulse referred to above is adequately short.

Referring now to FIGS. 4 and 5, when the bandwidth of the input pulses30 satisfying the critical condition is less than that of the resonance32, the output 34 is one or a sequence of Zn pulses (FIG. 4). However,when the bandwidth of the input pulse 36 is greater than that of theresonance 38, the output pulses 40, as a function of time, exhibitringing (FIG. and appear as oscillations having a changing period, whichmay be damped, or modulated.

Our calculations predict this effect under conditions when theoscillators are not excited weakly but very strongly, that is, in aregion where the pendulum does not oscillate with a constant period butwith a nonlinear period because of deviation pendulum in angle is notsmall. The oscillation period is changed and the initial amplitudeshould as well give information about the width of the atomic resonanceand about the concentration in some contour shape which would be relatedpartially to the shape of the input pulse. This is particularly true ifthe pulse width itself happens to be comparable to the dampening time ofthis pendulum.

It should be noted however that the invention is not limited withrespect to the shape of the input burst (pulse) except that the area, 6,whatever it is, is greater than 11 A, and satisfies the relaxationcondition of being less than the relaxation time of the resonant media.For example, let an initial pulse area appear in shape as though it werea sequence of very short pulses. If these pulses taken togethersatisfied the area therein and the duration condition, then theinvention predicts the area of the output pulse and predicts that itwill propagate through the medium. Our invention specifies the totalarea of the output signal. Accordingly, the invention specifies whathappens to the total area of the output signal, and is not specific toany particular pulse within that area, although, for simplicity, asingle input pulse has been described and is a special case.

FIGS. 38 and 3C show the type of propagation that results from pulseshaving areas significantly larger than 1r A. Thus, FIG. 3B shows aninput pulse of 2.911 area which reshapes into a 21: pulse as itpropagates through the resonant medium. In so doing, the peak electricfield and peak power increases, and the duration decreases. FIG. 3Cshows the reshaping of a 3.611 pulse into two 211' pulses, the first onehaving short duration and delay, while the other has an increasedduration and delay as it develops from a 1.617 pulse to a 21:- pulse.

EXPERIMENTAL EXAMPLE The predictions of the above modelsv have beenqualitatively confirmed by experiment. Referring to FIGS. 6 and 7, thereis shown the experimental apparatus by which the invention was put intopractice utilizing electromagnetic energy in the visible region. Thus,there is provided a laser source 42 having an output burst pulse 43which is controllable in amplitude and duration by suitable burst widthand amplitude controls 44, 46 provided on the apparatus. The burst pulse43 from the laser passes successively through an optically alignedsystem including an attenuator 48, a resonant medium 50, an attenuator52 and a photosensor 54 which may be a photographic camera. The resonantmedium 50 consisted of an elongate rod of ruby having the composition0.05 percent chromium Cr" in a crystal of Al O The rod had dimensions ofone-half inch in diameter and 2 inch in length and had a relaxation timeT 10" seconds and was cooled in apparatus 56 to liquid heliumtemperature. FIG. 7 shows the energy level diagrams for the source andthe resonant medium.

The laser source 42 was a Q-switched liquid nitrogen cooled ruby lasersfltably controlled to provide only the plane polarized E (2E) 3 4At3/2) output laser line. By thermal tuning this transition it was maderesonant with the 4A (il/2) 2 Ems transition of the resonant medium 50with its optical C axis in the z direction. Input energies ranged fromabout 3 millijoules at 10 nanoseconds for delay experiments to 5millijoules at 20 nanoseconds for transmission threshold studies.

FIG. 8 illustrates the nonlinear transmission effect for various inputlight intensities into the resonant medium of FIG. 4. Weak light, wellbelow the onset of nonlinear transmission, was attenuated by more than afactor of 10 The graph reveals there is a reduction or attenuation by afactor of 4 in the output pulse energy for a change in input energy of afactor of 6. The vertical bars represent the magnified output which ismeasured by attenuation until photographic film is unexposed, anddetermines the peak transmitted energy per square centimeter. Thevertical bars also indicate the experimental error assumed to be due tooutput fluctuations probably caused by uncontrolled characteristics ofthe ruby laser source and the step type output attenuation calibration.The dashed line represents the expected response if a lineartransmission law were applicable.

FIG. 9 shows the modified arrangement of the apparatus which was used tocompare the input and output signal pulses as applied to the medium.Thus, the apparatus is similar to that shown in FIG. 6 including lasersource 42 arranged to provide output coherent light burst pulsesdirected into resonant medium 50 of a ruby rod. A half mirror beamsplitter 60 intercepts a portion of the laser input pulse 43 and sendsit to the photodiode detector 62. A mirror 64 directs the output lightpulse passed by medium 50 to detector 62 so that the detector output isresponsive to both the input and output light pulses. The detectorconverts the light burst pulses into pulses representing the envelope ofthe signals which are then displayed on an oscilloscope 66 as a functionof time.

FIGS. 10A, B and C show the oscilloscope traces for various experimentalconditions using the arrangement of FIG. 9. FIG. 10A shows the input andoutput pulses with the medium 50 at room temperature. Since the pulseswere coincident a delay was used to separate the two pulses, the secondof which travelled through the medium 50. In the graph of FIG. 103 themedium has been thermally cooled by liquid helium temperatures. Asshown, the pulse which has travelled through the medium has been delayedthereby (no other delay was used).

FIG. 10C shows the output pulse wave shape and il- Iustrates agreaterdelay caused by increasing width of the input pulse. The delay ofthe pulses is qualitatively in accordance with equation (10) since itincreases with pulse width.

For the particular transitions used in this experiment the transmissioneffect of the invention diminishes with increasing sample temperature,disappearing completely at 40 K, where the rapid Orbach relaxationbetween the upper levels 2/! (2E) 2 E (2E) imposes a condition T Z r,.At the same time the thermal shift of the optical resonance only amountsto about one-fourth of a linewidth and the light is nearly completelyattenuated.

The transmission behavior might be interpreted as an effect in which theabsorption line is saturated by the leading edge of the pulse, sometimestermed hole burning. However, a population rate equation description ofthe above experimental observations would not be valid because dampingtimes are long at liquid helium temperatures for ruby, and the largepulse delay times cannot be counted for by a rate equation model.

ENERGY TRANSMISSION SYSTEM Referring to FIG. 11 there is shown theapplication of the invention to the transmission of electromagneticenergy over long distances and through atmosphere which may containclouds, fogs, or other absorbing media. Thus, there is provided acoherent electromagnetic energy source 70 such as a maser capable ofdelivering output bursts 72 of coherent electromagnetic energy. Thebursts can be made adjustable with respect to amplitude and duration ashereinbefore described so that the critical conditions can be achieved.There is also provided a receiver 74 of electromagnetic energy which canbe of any suitable type. The source 70 and the receiver 74 are suitablymounted in line of sight locations such as atop high structures ornatural sites which are spaced apart a considerable distance.

Means is provided for imposing a signal on the pulses being transmittedthrough the medium and can consist of conventional means for varying thepulse width, the intensity, or the polarization of the pulses in such amanner that selected pulses do not satisfy the propagation conditionwhile others do.

Specifically, there is provided a programmer 76 which supplies triggersignals to cause the laser to put out a sequence of pulses which areplane polarized or are passed through a polarizer 78. The pulses thenpass through a Kerr cell 80 which is controlled by programmer 76 so thatselected pulses are eliminated by crossed polarization. In this way, thetransmitted pulses can be modulated by conventional methods such aspulse position modulation (PPM), pulse count modulation (PCM), and pulsefrequency modulation (PFM). Because the individual pulses satisfy thecritical propagation conditions as to duration and strength for theinterfering weather, the information thereon will pass through suchweather without being absorbed out and the transmission link will bemaintained.

DELAY, STORAGE, AND LOGIC SYSTEMS A most useful property of theinvention is the time delay which is imposed upon the coherent pulse asit passes through the medium. For a given pulse width r,,, the timedelay T is given roughly by T=L/v=L l2 where L is the medium thicknessand a is the classical optical absorption coefficient which would applyto the absorption of an ordinary weak pulse of incoherent or coherentlight. Depending upon the size of a, light time delays of Tapproximately to 10' seconds are readily achievable. Accordingly, theapparatus of FIG. 6 is also a delay line in accordance with the length Lof the resonant medium through which the pulses pass.

Referring to FIG. 12, there is shown apparatus in which the amount ofthe delay is varied with a fixed medium 82 of given length by applying avarying biasing magnetic field to the medium with a coil 84 and currentsource 86 in order to change the variable g(0). This variable isproportional to a and which represents the population of excitablespecies at a particular frequency. When the biasing magnetic field isapplied to the medium a greater delay is encountered since fewerexcitable species are available due to the broadening of the resonanceline shape of the medium.

The delay may also be varied by the means for changing the pulseintensity as applied to the medium or its duration as in FIG. 6. It isfound that shorter pulses propagate faster through the medium. Asillustrated in FIG. 1, pulses having areas between 2,r and 3,, shortenin duration as they pass through the medium in order to obtain the 21Tcondition. Accordingly, by varying the pulse amplitude and its durationthe delay also varies.

The delay line apparatus of FIG. 12 can be operated to provide a shorttime storage element for use with optical pulses. If source 86 issufficiently energized, the medium and bias field can be selected sothat a magnetic shift off resonance occurs by an amount sufficient tomake the medium transparent to the pulses. Thus, a series of pulses maybe introduced into the medium wherein they are delayed for short times.When it is desired to obtain the pulse stored in the medium as an outputthe resonance shifting field is applied so that the material becomestransparent. FIG. 13 depicts the delay per unit length as function oftime and shows that upon application of the field, at time t, the mediumbecomes transparent and the pulses stored become immediately availableat the output.

FIG. 14 shows a light delay line apparatus in which the output of thelaser source is passed through a means for varying the beam crosssection such as a zoom lens 88 having a variable focal length afterwhich it impinges upon the resonant medium 90. When zoom lens 88 expandsthe beam cross section, the delay will increase as the power densitydecreases. By increasing the power density the critical condition can beexceeded and the output varied even to the point of producing multipleoutput pulses.

MULTIPLE DELAY AND STORAGE Referring to FIG. 15, there is shown a systemin which delayed light pulses are stored as a digital information andselectively retrieved. Thus, there is provided a laser source 92 whichis pumped to provide a coherent light output pulse 94 satisfying thecritical conditions previously described. The output pulse is directedthrough one channel of a resonant medium 96 which is identified aschannel 96-7. After passing through channel 96-7 it is reflected in turnby mirrors 98, 100, 102 and 104 into an almost rectangular race. Themirrors are so positioned that the light pulses successively passthrough adjacent channels 96-6,..., 96-1 of media 96. Mirrors 98 and 100are partially transmissive so that certain of the pulse information willbe passed through such mirrors. Partially reflective mirror 98 serves topermit a portion of the pulse to be passed onto detector 106-7 whichregisters as a pulse number 7 early in time t. Detector 106 providesinformation regarding the existence of a pulse in any channel at anyparticular time.

A portion of the pulse can also be transferred through the beam splitteror partially reflective mirror 100 to concentrating lens 108 to impingeon detector 110 as shown. The output detector 110 is the sum of allchannels at a particular time. The remainder of the pulse is deflectedby mirror 100 and passed on channel 6 through the resonant medium onchannel 96-6 so that the process which effected the pulse on path 7 noweffects the pulse on channel 6 except that there has been introduced adelay. The relative delay between the various pulses in channels 1 to 7is variable as by varying the input pulse widths or by biasing, ashereinafter explained. After the pulse has passed through all thechannels, it is permitted to leave the race and impinge upon detector111, the output of which is a real time output of the pulses passingthrough the apparatus.

The presence or absence of a pulse can be predetermined by whether ornot the medium is sufficiently coherent in response with respect to thepulses. Thus, the medium 96 can be modulated as by applying biasmagnetic fields thereto with current sources 112- 1...ll2-7 and coilsl14-l...1l4-7 in the manner previously described in connection with theembodimentof FIG. 12. Alternatively, the incoming pulses can beindividually modulated in intensity, phase, or sense of polarization inorder to achieve a desired pulse modulation of the output. Accordingly,the above system is useful for storing digital information in lightpulse form and for retrieving it.

OPTICAL LOGIC Referring particularly to FIG. 16 there is shown apparatusfor performing logic functions with a form of the invention operating inthe optical region. Thus, there is provided a coherent source 120 whichis coupled to the inputs of parallel optical signal paths 122 and 124.After the light traverses either of the optical signal paths 122 and 124it is passed into a resonant medium 125 so that the light cooperates toproduce a pulse within the medium which is the sum of the input pulses.The output of the resonant medium is passed to a receiving mechanism 126which may be a light detector but which would usually be downstreamportions of a computer system.

In operation, the coherent source generates light pulses having a valuesuch that there is selectively created in each of the optical signalpaths pulses having an area of less than 7r, say for example 3/4 asshown but a duration shorter than the relaxation time. If each of theinput signals is energized to permit passage of the pulses, they willappear at the input face 128 of the resonant medium, (a pulse having anarea of sufficient magnitude to develop at 1 A,, greater than rr+ A).Such a pulse will propagate and become a 2,, pulseas it passes throughthe resonant medium and will .be received by the receiver. If, however,either or both of the inputs A and B are not present the respectiveresonant medium will absorb whichever pulse is present because itabsorbs any single pulse having an area less than 11'. Accordingly,there has been shown an optical realization of an AND logic gate. As iswell known, the use of De- Morgans theorems, permits the construction ofa complete Boolean logic system from this single realization (AND).

If one pulse were made to have a very short duration,

' it would travel faster through the resonant medium 125 and accordinglywould combine with an already present pulse of longer duration anddelay. The latter could be termed the stored pulse. In such aninteraction the short, second pulse would take up energy from the firstpulse and step on ahead of it. Furthermore, in again reestablishing the2 it would have to shorten its duration. For this reason it would travelfaster than otherwise and its time of arrival at the output could betaken as a direct logic function indicative of both signals.Additionally, such a scheme eliminates the need for simultaneoussignals.

PULSE SHAPERS In general, the pulse passing through the resonant mediumwill be affected in many of its properties in accordance with the natureof the medium. This leads to a class of devices which are termed pulseshapers and which include mechanisms for changing the intensity, shapeand frequency content of the light pulse that passes through theresonant medium. The following operations may be carried out with theapparatus of FIG. 12.

Referring to the graphs shown in FIGS. 3A, 3B, 3C, it

is noted that a pulse having an area lying between 1r and 2,r isgradually developed into a pulse having an area 2,, after a shortdistance of propagation through the medium. In this case, the pulseduration is broadened as shown by the graphs 3B and the intensitydecreases. Accordingly, if it is desired to reduce theintensity of apulse and/or to increase its duration, it may be applied to a suitablyselected medium in which it is a pulse having an area lying between 1r Aand Zn, and a duration less than the relaxation time. After a suitabledistance through the medium, it will have been changed to a differentshape in the manner shown in FIG. 3B. Furthermore, the exact desiredpulse shape can be obtained by operating the material in resonance for apredetermined period of time and then applying a resonance shiftingfield to the medium so that it becomes transparent and permits the pulseas it exists in its then modified form to appear at the output of thematerial.

Referring to the graph shown in FIG. 3C wherein a 2.91: pulse is appliedto the medium, it is shown that this pulse will propagate and become a2n pulse. In so doing, the pulse intensity will increase so that itspeak power will also increase. Simultaneously duration of the pulse willdecrease. As a consequence, the pulse may be changed to provide greaterpeak powers and shorter durations. As mentioned above, the amount of thechange may be controlled by operating with a medium capable of beingdriven off resonance so as to become transparent to the pulse at anytime whereat the pulse has the desired shape.

The above effects can be utilized as a collimating or focusing device inthe following manner. Assume that the initial light pulse is focusedinto a converging beam as it enters the resonant medium. In this case,the area of the pulse will tend to increase as it proceeds into themedium. But, a relationship exists between the nature of the focusingand the corresponding change in pulse power. This follows from the factthat the input pulse tends to maintain an area even though the intensitytends to change due to focusing. For the 27: pulse to be maintainedwhere the light pulse was originally converging, the resonant mediumwill cause the light pulse to diverge. The converse argument shows thatdiverging light pulses will be focused or converged. Accordingly," themedium will serve to collimate converging or diverging light pulses.

MICROWAVE APPLICATIONS A little consideration will show that tliesystems and apparatus disclosed herein can be realized withelectromagnetic traveling waves interacting with resonant mediaoperating in the microwave region. Thus, there is a strict analogybetween microwaves in guided structures such as waveguides and theformula is developed in analyzing light waves. Consider microwavetransmission in a waveguide assumed to be lossless and empty. The fieldsare given by the I I(x,y,z,t) I I(x,y) cos (wt kz) h,,(z,t) where I?describes the mode in which the guide is operating and k w/V to beingthe frequency and V is the phase velocity. It is also assumed that w isnot near a cut-off frequency (i.e., V is roughly constant with respectto m. Considering only the forward traveling wave, h,,(z,t) which ismodified from its constant value in the empty lossless guide to obey theequation where m( ,r)

EfM'E (z, y) dxdy.

M is a pseudomagnetic (or electric) moment which radiates to change h,,.The equations describing m are the Bloch equations. If a sample issituated so that H (x,y) is almost constant over the sample, theseequations will involve only the absolute value of H(x,,,y,,) togetherwith a coupling constant describing the samples interaction with themagnetic field. Under these conditions the equations found will conformto those previously described with respect to light, with appropriatedefinitions.

To be more specific, the following example is given with respect to amicrowave delay line utilizing the principles of the invention.Referring to FIG. 17 there is shown a generator 130 of coherentmicrowave energy which directs the same through variable attenuator 132.The output of the attenuator passes through a microwave waveguidesection 134 which contains a resonant medium 136 having a relativelysmall cross section and located in a region of substantially uniformmagnetic field. As the microwave energy propagates through thewaveguide, it will be delayed due to the action of the resonant mediumdepending upon the amount of attenuation introduced by the variableattenuator. If desired, the medium can be magnetically biased with acurrent source 138 and coil 140 in order to broaden the line width ofthe response. In many cases, medium 136 can also be constructed of ruby.

The apparatus of FIG. 17 permits the invention to be carried out in themicrowave spectrum.

FREQUENCY FILTERING AND MODULATION In addition to the above theinvention is also applicable as filtering and frequency modulationdevice. Referring to FIG. 18A shows a graph of the spectrum a of theinput frequency applied to a resonant medium in the manner of theinvention as for example in the arrangement of FIG. 6. Spectrum 150acontains noise components as well as a range of frequency about theresonance 151a. It is found that the resonant medium eliminates thosefrequency components within the pulse which are significantly off of theresonance of the medium and which may include a large component ofnoise. The spectrum 152a of the output pulse is shown in FIG. 18B andhas a narrower frequency content without the noise.

Referring to the graph of FIG. 19, when utilizing a suitable means forshifting the resonance line l5lb to l5lc in the resonant medium such asby magnetically biasing the same as in the apparatus of FIG. 12, thefrequency content of the output pulse 152b tends to shift 152C with theresonance l5lc so that frequency modulation of the output is achieved.

THRESHOLD SIGNAL DETECTOR The frequency filtering property and pulsereshaping property is of direct applicability to low signal microwaveradar detection. Background clutter noise or jamming noise can beeliminated by preamplification of the radar return pulses and injectingthem into a microwave resonant medium tuned to the radar frequency. Forpulse areas exceeding 1r, heretofore described, the noise will beeliminated at the output of the medium.

For weak communication and radar signals containing low coherent power,comparable to noise, a threshold signal detector is operated as follows:

Let an internally generated microwave pulse of area 11 A, slightly lessthan 1r, be injected into a resonant medium at the receiving station.Let A be very small, so that if any radiation pulse received externally,to be detected, exceeds the area A, it will then add to the internallygenerated pulse area coherently to permit the traveling wavetransparency condition (area 1r) to take over. The appearance of theoutput 21: pulse at the output of the resonant medium specifies thetrigger threshold detection" of the very weak input signal. Moreover,the internally generated pulse may be used to add to weak incomingcontinuous wave signals, as well as pulse signals, and the onset of 'thetransparency condition again signifies detection of the weak inputsignal.

The above signal detection scheme, of course, can be applied with thesame logic to the detection of weak coherent light signals, pulsed orcontinuous wave. Apparatus for carrying out the above operations wouldbe similar to that shown in FIG. 16, one signal path 122 being from thesource to the medium 125, on which the 11' A pulse would travel, theother path 124 being modified to include the low level signal pulsebeing sought.

PROPERTIES OF MATERIALS The present invention has immediate applicationto the investigation of the properties of materials especially solidswhich have theretofore been impossible to directly investigate becauseof resonant abosrption. Referring to FIG. 20 there is shown apparatusfor car rying out such investigations with laser light and consists of alaser 160 and power source 162, the output pulse 163 of laser 160 ispassed through a modifier 164 which serves to vary the frequencycontent, pulse width, intensity, polarization, focusing, shape or otherproperty of the output of the laser. The modified pulse 165 is passedthrough the sample medium 166 understudy and the output pulse 167 frommedium 166 is applied to a detector 168. The Detector 168 supplies anelectrical signal 169 indicative of the envelope of the received signalwhich can be coordinated with the input signal via suitable programmerand computer 170 which operates to control and coordinate the entireapparatus. Unit 170 controls the modifier 164 and the laser power source162 and correlates the pulses received from the detector with the inputlaser pulsing source to thereby correlate the analysis of the medium 166under study. The following operations can be carried out utilizing theapparatus and arrangement of FIG. 20.

Means 169 is provided for changing the temperature, pressure, or otherthermodynamic properties of the material being investigated. Means 169can also be used for applying electrical or magnetic fields in order tocarry out analysis of the physical changes induced thereby in thematerial. A suitable means can be provided for changing the dipolemoment of the sample material which can find importance in analyzing avariety of gases such as the metastable states in mercury vapor and insolids such as CR 3 in magnesium oxide.

MEASUREMENT OF THE WIDTH OF THE RESONANCE LINE OF A OPAQUE MATERIALAssume that a crystal satisfying the conditions set forth above which isnormally opaque and has a resonance line which it is desired toinvestigate. Referring again to the graph shown in FIG. 4, when theinput pulse bandwidth is considerably less than the resonance bandwidthof the material under investigation. In this situation, the outputappears as a single 21r pulse as previously discussed. As the bandwidthof the input pulse is increased considerable changes begin to take placeas it approaches the bandwidth of the resonance line. Taking for examplea limiting case, as shown in FIG. 5, wherein the bandwidth of the inputpulse is broader than the resonance line, the output will consist of aseries of pulses lying in an envelope which is decreasing. The series ofoutput pulses resembles damped ringing phenomenon. The resonancebandwidth of a medium under investigation can thus be directly measuredby noting the onset of perturbations in the output and the developmentringing as the input bandwidth approaches and exceeds the resonance linebandwidth.

MEASUREMENTS OF DOPING UNIFORMITY IN THE SEMICONDUCTORS In themanufacture of semiconductor devices, it is often desired to uniformlydope a volume of the semiconductor with an impurity so as to change itsconductivity properties. Often such impurities fail to become uniformlydisbursed but rather settle into cracks or imperfections in the crystal.These effects can be exceedingly small and not directly observable. Sucha concentration of dopant impurities results in inhomogeneous broadeningof the resonance line of the material as contrasted to the homogeneousbroadening which results from the uniform dispersion. In the homogeneouscase, true relaxation exists so that the duration of an input pulsewhich proceeds unattenuated through the sample would have to be madeconside'rably shorter than the inhomogeneous case. In practice, it ispossible to develop a reference relaxation time associated withinhomogeneous broadening which time is significantly shorter than thatassociated with the homogeneous case. Accordingly, samples of normallyresonantly opaque semiconductive material can be investigated inapparatus of FIG..20 by using them as the medium and varying theduration of the input pulses. In this way the relaxation time will bedetermined when the duration of the input pulse becomes comparable tothe damping time of the sample medium under investigation. This servesas a measure of the degree of perfection in the distribution of theimpurity dopants.

SEPARATION AND MEASUREMENT OF SUPERIMPOSED OR OVERLAPPING RESONANCELINES In many materials there exist adjacent resonances which mayoverlap or lie within each other, that is to say, be superimposed. Inthis situation it is extremely difficult to detect and measure thecharacteristics of one type of resonance separatelyfrom the other. Thepresent invention is able to separate these resonance lines under manyconditions of which the following are examples.

Assume the existence of a crystal with two dopant impurities, one ofwhich promotes a broad resonance and the other a narrow resonance whichmore or less coincide or overlap. It will be recalled that the dO/dzcoefficient 0 is defined by the dipole moment of the particularresonance. Consequently, what is a 2n pulse for one resonance is in mostinstances not of the same magnitude as the 21: pulse for the otherresonance. Accordingly, the resonance can be separated by sweeping thefrequency across the broad resonance and measuring the area of the pulsepassing through the resonance material. If the adjustment is made suchthat the area of the pulse is 21r for the broader resonance, this pulsewill be insufficient when part of its area contributes to exciting thenarrower resonance. At this point the pulse will no longer satisfy the211' condition so that various changes will take place. Possibly theremay be area to excite both resonances in which case a pair of 211'pulses will be formed probably having different kinds of delays anddurations. Another possibility is that enough of the pulse would betaken into the second resonance that the 1r A condition for the area ofthe pulse would not be satisfied for either of the resonances. In thelatter case, the strong attenuation would take place.

The above scheme is directly applicable in the study of semiconductormaterials. Often there is band absorption by energy levels which arequite closely situated. Where the energy levels are due to splitting inthe ground state, the situation is the same as that posed by the use oftwo different dopant impurities having closely spaced ground states, asset forth above.

If the dopant impurities or the medium in general present more than twoquantum levels for each ground state to the incoming wave, sometransitions may be close to exact resonance, while simultaneously othertransitions are farther off resonance. The net effect upon the incomingpulse of a specific frequency will be to parcel its energy (among allthe quantum states) into a superposition of absorption and emissioncycles which will impose a final characteristic of pulse shaping andattenuation on the output pulse. The final effects on the pulse willcharacterize the specific character of the absorbers and the crystalsymmetry of the host medium. In certain situations the final output willconsist of a plurality of pulses at separate carrier frequenciescorresponding to the separate quantum transitions of the absorbingatoms.

In summary, the output for a given frequency sweep across the resonanceswould result in two cases, one in which the output would consist of twodifferent pulses at two different frequencies and at different delays.In the other case the output would be of a single frequency andattenuated. In the latter the analysis of the pulse would provideinformation about the resonances since on the low frequency side thearea of the Zn pulse defined by the resonance would be different in mostcases from that defining the area of the 21r pulse for the otherresonance. For example, in the ruby resonances referred to in the mediumof FIG. 7, the areas of these resonances differ by a factor of about 50percent.

To those skilled in the art to which this invention relates many otherchanges, modifications and applications of the invention will suggestthemselves. For example, many other properties of materials can beinvestigated by using the invention. By way of example, there existcrystalline solids which are normally opaque, and which possessbirefringence which can be studied by using polarized light pulses asdescribed herein. Accordingly, the description and disclosures containedherein are to be taken as illustrative of the invention and not as alimitation thereon.

We claim:

1. In a method for propagating periodically varying electromagneticwaves through a medium exhibiting a resonance response to such waves andtherefore normally opaque to such waves, the steps of forming a coherentpulse of said electromagnetic waves, said pulse being composed of waveshaving a frequency content capable of coupling to said resonanceresponse, limiting the product of the strength of said pulse and itsduration in accordance with the equation where 1r=3.l4l6..., E is theelectric field strength of said waves, and t is the duration of saidpulse to a value less than the relaxation time of the response of saidmedium, and applying one or more of said pulses to said medium.

2. In apparatus for propagating periodically varying electromagneticwaves through a medium exhibiting a resonance response to such waves andtherefore normally opaque to such waves, means for generating a coherentpulse of electromagnetic energy composed of waves having a frequencycontent capable of coupling to said resonance response, means forcausing the output of said generator to occur in pulse-like burstshaving the property that the product of the strength of said pulse-likebursts and its duration is limited in accordance with the equation where1r=3.l4l6..., E is the electric field strength of said waves, and t isthe duration of said pulse-like burst, in which said pulse is furthercharacterized by having a duration less than the relaxation time of theresponse of said medium.

3. Apparatus as in claim 2 in which said generator is a ruby laser andin which said medium is a ruby rod normally absorptively resonant to theoutput of said laser.

4. Apparatus as in claim 2 further including a receiver responsive tosaid electromagnetic waves and means for mounting said receiver in analigned position with respect to said means for generatingelectromagnetic energy for receiving said electromagnetic waves at alocation spaced apart therefrom.

5. In apparatus for delaying electromagnetic waves, means for generatingcoherent electromagnetic waves, a medium exhibiting a resonance to suchwaves but transmissive to bursts of said electromagnetic waves wheneverthe product of the strength of a pulse thereof and its duration islimited in accordance with the equation when 1r=3.l4 l 6..., E is theelectric field strength of said wave, and t is the duration of saidpulse, and wherein the duration of said pulse is limited to a value lessthan the relaxation time of the response of said medium, means mountingsaid generator so that said pulse is passed through a predeterminedlength of said medium.

6. Apparatus as in claim 5 further including means for varying the delayof said waves through said medi- 7. Apparatus as in claim 6 in whichsaid means for varying the delay includes means for broadening theresonance and bandwidth of said medium.

8. Apparatus as in claim 7 in which said means for broadening theresonance bandwidth includes means for magnetically biasing said medium.

9. Apparatus as in claim 6 wherein said means for varying the delayincludes means for shortening the duration and increasing the strengthof said pulses.

10. Apparatus as in claim 6 wherein said means for varying the delayincludes means for changing the pulse cross section.

11. Apparatus as in claim 10 wherein said means for generating coherentelectromagnetic waves comprises of a laser having an output beam and inwhich said means for changing said pulse cross section includes a lenshaving a variable focal length for varying the divergence of said laserbeam whereby the delay increases as the power density is decreased bysaid lens.

12. Apparatus as in claim further including means for defining aplurality of channels through said medium, means for recycling a pulsethrough said plurality of channels, and means for extracting pulses fromsaid channels.

13. Apparatus as in claim 12 further including means for selectivelyshifting the resonance line shape of at lease one of the channels ofsaid medium.

14. In apparatus for performing a logic operation, a coherentelectromagnetic wave generator, a medium normally absorptively resonantto electromagnetic waves of a predetermined frequency generated by saidgenerator but transmissive bursts of coherent electromagnetic waveswherein the product of the strength of a pulse of said waves and itsduration is limited in accordance with the equation where 'n'=3.l4l6...,E is the electric field strength of said wave, and t is the duration ofsaid pulse, and further limited such that the duration of said pulse isless than the relaxation time of the response of said medium, meansforming two signal paths between said generator and said medium, saidsignal paths having outputs directed toward an input of said medium sothat the outputs of said signal paths cooperate thereat to produce apulse within the medium which is the sum of the signals traversing saidpaths, means controlling the level of the signals within said paths sothat the pulse area thereof is less than 1r so that, whenever bothsignals are present, a combined signal is produced having a strengthgreater than 1r which then propagates through the medium, and whenevereither of said input signals is present alone it is attenuated by theresonant medium and no output pulse is emitted.

15. In pulse shaping apparatus for modifying electromagnetic waves,means for generating bursts of coherent electromagnetic waves, a mediumnormally absorptively resonant to electromagnetic waves of apredetermined frequency generated by said last named means buttransmissive to bursts thereof characterized by the product of thestrength of said burst in its duration being limitedin accordance withthe equation where 'rr=3.l4l6..., E is the electric field strength ofsaid wave, and t is the duration of'said pulse, and further in which theburst is limited to a duration less than the relaxation time of theresponse of said medium, means mounting said generator so that saidpulses pass through a predetermined length of said medium, pulses havingan area lying between 1r and Zn being increased in duration anddecreased in intensity as they are passed through the medium whilepulses having an area lying between 21r and 3w being increased inintensity and shortened in duration.

16. Apparatus as in claim 15 further including means for shifting theresonance of the medium so that it becomes transparent to permit thepulse as rr to exist in its modified form in a particular time to appearat the output ofthe device.

17. In apparatus for changing the convergence and divergence ofelectromagnetic waves, means for generating bursts of electromagneticwaves having a predetermined frequency and including means for limitingthe product of the strength of said burst in its duration in accordancewith the equation where 1r=3.l416, E is the electric field strength ofsaid wave, and t is the duration of said pulse, a medium normallyresonant to said traveling electromagnetic waves said means forgenerating said coherent electromagnetic waves further including meansfor limiting the duration of said pulse to a value less than therelaxation time of the response of said medium and for applying saidbursts to said medium so that said waves propagate through the medium,whereby diverging or converging electromagnetic energy within saidbursts are collimated by said medium. 7

18. In a method for detecting low level electromagnetic signals thesteps of providing a medium exhibiting resonance response toelectromagnetic energy of a predetermined frequency and thereforenormally opaque to such electromagnetic waves, forming coherent pulsesof electromagnetic waves of said predetermined frequency, limiting theproduct of the strength of said pulse and its duration to a value inaccordance with the equation to slightly less than 11 where1r=3.l4l6..., E is the electric field strength of the applied pulse, andt is the duration of said pulse and further limiting said pulse to avalue less than the relaxation time of the response of said medium,applying said pulses to said medium, further applying the low level tobe detected to said medium so that said pulse and said low level signalcombine to create a pulse within the medium in which the combined pulsesatisfies the criteria KI Edt 1r (where E includes both pulse and signalcomponents) whereby the absence of said low level signal is indicated bythe absence of an output pulse from the medium and the presence of saidlow level signal being sufficient to induce said medium to propagate thecombined signal so that the presence of'an output pulse from the mediumis indicative of the existence of a low level signal applied to theinput.

19. A method as in claim 18 wherein said signals are microwave signals.

20. Apparatus for investigating the properties of materials comprisingagenerator for providing an output of coherent electromagnetic wavessaid generator including means for varying the pulse duration andintensity of the output of said waves as over a range including whereinbursts are formed characterized by a predetermined frequency content andhaving the property that the product of the strength of said burst andits duration is limited in accordance with the equation where 1r=3.14l6,E is the electric field strength of said waves and t is the duration ofsaid bursts and further including means for limiting the duration ofsaid bursts to a value less than a predetermined time of an exptectedvalue corresponding to the relaxation time of the material to beinvestigated so that the bursts are applied thereto, means for detectingthe amount remaining of said bursts which have passed through thematerial.

21. Apparatus as in claim further including a programmcr and computerfor controlling and coordinating the apparatus to record the variationin intensity and pulse duration of bursts applied to the sample mediumunder investigation as a function of the output response from the samplemedium.

22. Apparatus as in claim 20 further including means for sweeping thefrequency of the output bursts across a predetermined bandwidth offrequencies.

23. Apparatus as in claim 20 further including means for varying athermodynamic variable of the material under investigation so that thechanges of the transmission properties of the material can be measuredand correlated with the changes in the material due to varyingthermodynamic variables.

24. A method for measuring the bandwidth of a resonance exhibited by amaterial, said resonance relating to a response to electromagnetic wavesso that said material is normally opaque thereto, the steps of formingand applying to said material coherent pulses of said electromagneticwaves each pulse being composed of waves having a frequency contentcapable of coupling to said resonance response, limiting the product ofthe strength of said pulse and the duration thereofin accordance withthe equation where 1r=3. 1416, E is the electric field strength of saidwaves, and t is the duration of said pulse, further limiting theduration of said pulse to a value less than the relaxation time of theresponse of said medium, subsequently increasing the frequency bandwidthof the input pulses to said material and noting the onset perturbationsin the waves transmitted by said medium as the input bandwidthapproaches the resonance bandwidth.

25. A method for measuring the uniformity of doping of a volume ofsemiconductor having an impurity therein comprising the steps ofmeasuring the relaxation time of a uniformly doped referencesemiconductor sample by applying a coherent traveling electromagneticwave pulse to said semiconductor sample said pulse being furthercomposed of waves having a frequency count capable of coupling to theresonance of said sample and limiting the product of the strength ofsaid pulse in its duration in accordance with the equation where1r=3.l4l6, E is the electric field strength of said waves, and t is theduration of said pulse, and further limiting the duration of said pulseto a value less than the relaxation time of the response of saiduniformly doped semiconductor, thereafter increasing the duration ofsaid pulse until it is attenuated due to the homogeneous doping of saidsemiconductor to thereby define a reference relaxation time, applyingcoherent electromagnetic pulses of energy to successive samples ofsemiconductor material in which said pulses are also characterized bythe equation and a duration slightly less than said reference time, andnoting those samples under test which absorbed an input pulse suchabsorption being indicative of inhomogeneous broadening due to imperfectdistribution of the dopants within said sample.

26. In a method for varying the shape of an electromagnetic wave thesteps of passing said wave through a medium exhibiting a resonance tosuch waves, forming a coherent pulse of said waves having a frequencycontent capable of coupling to said resonance response of said medium,limiting the product of the strength of the pulse and its duration inaccordance with the equation KL": Edi 11 where F3.1614, E is theelectric field strength of said waves and t is the duration of saidpulse limiting the duration of said pulse to a value less than therelaxation time of the response of said medium and applying said pulsesto said medium, said medium serving to reform said input pulses intooutput pulses satisfying the equation Edi=21r K Edt 7r where 11'3.l4l6..., E is the field strength of said waves, and t is the durationof said pulse to a value less than the relaxation time of the responseof said medium, and applying one or more of said pulses to said medium.

28. In an apparatus for propagating periodically varying electromagneticor sound wavesthrough a medium exhibiting a resonance response to saidwaves and therefore normally opaque to such waves, means for generatinga coherent pulse of said waves having a frequency content capable ofcoupling to said resonance response, means for causing the output ofsaid generator to occur in pulse-like bursts having the property thatthe production of the strength of said pulse-like bursts and itsduration is limited in accordance with the equation

1. In a method for propagating periodically varying electromagnetic waves through a medium exhibiting a resonance response to such waves and therefore normally opaque to such waves, the steps of forming a coherent pulse of said electromagnetic waves, said pulse being composed of waves having a frequency content capable of coupling to said resonance response, limiting the product of the strength of said pulse and its duration in accordance with the equation where pi 3.1416..., E is the electric field strength of said waves, and t is the duration of said pulse to a value less than the relaxation time of the response of said medium, and applying one or more of said pulses to said medium.
 1. In a method for propagating periodically varying electromagnetic waves through a medium exhibiting a resonance response to such waves and therefore normally opaque to such waves, the steps of forming a coherent pulse of said electromagnetic waves, said pulse being composed of waves having a frequency content capable of coupling to said resonance response, limiting the product of the strength of said pulse and its duration in accordance with the equation where pi 3.1416..., E is the electric field strength of said waves, and t is the duration of said pulse to a value less than the relaxation time of the response of said medium, and applying one or more of said pulses to said medium.
 2. In apparatus for propagating periodically varying electromagnetic waves through a medium exhibiting a resonance response to such waves and therefore normally opaque to such waves, means for generating a coherent pulse of electromagnetic energy composed of waves having a frequency content capable of coupling to said resonance response, means for causing the output of said generator to occur in pulse-like bursts having the property that the product of the strength of said pulse-like bursts and its duration is limited in accordance with the equation where pi 3.1416..., E is the electric field strength of said waves, and t is the duration of said pulse-like burst, in which said pulse is further characterized by having a duration less than the relaxation time of the response of said medium.
 3. Apparatus as in claim 2 in which said generator is a ruby laser and in which said medium is a ruby rod normally absorptively resonant to the output of said laser.
 4. Apparatus as in claim 2 further including a receiver responsive to said electromagnetic waves and means for mounting said receiver in an aligned position with respect to said means for generating electromagnetic energy for receiving said electromagnetic waves at a location spaced apart therefrom.
 5. In apparatus for delaying electromagnetic waves, means for generating coherent electromagnetic waves, a medium exhibiting a resonance to such waves but transmissive to bursts of said electromagnetic waves whenever the product of the strength of a pulse thereof and its duration is limited in accordance with the equation when pi 3.1416..., E is the electric field strength of said wave, and t is the duration of said pulse, and wherein the duration of said pulse is limited to a value less than the relaxation time of the response of said medium, means mounting said generator so that said pulse is passed through a predetermined length of said medium.
 6. Apparatus as in claim 5 further including means for varying the delay of said waves through said medium.
 7. Apparatus as in claim 6 in which said means for varying the delay includes means for broadening the resonance and bandwidth of said medium.
 8. Apparatus as in claim 7 in which said means for broadening the resonance bandwidth includes means for magnetically biasing said medium.
 9. Apparatus as in claim 6 wherein said means for varying the delay includes means for shortening the duration and increasing the strength of said pulses.
 10. Apparatus as in claim 6 wherein said means for varying the delay includes means for changing the pulse cross section.
 11. Apparatus as in claim 10 wherein said means for generating coherent electromagnetic waves comprises of a laser having an output beam and in which said means for changing said pulse cross section includes a lens having a variable focal length for varying the divergence of said laser beam whereby the delay increases as the power density is decreased by said lens.
 12. Apparatus as in claim 5 further including means for defining a plurality of channels through said medium, means for recycling a pulse through said plurality of channels, and means for extracting pulses from said channels.
 13. Apparatus as in claim 12 further including means for selectively shifting the resonance line shape of at lease one of the channels of said medium.
 14. In apparatus for performing a logic operation, a coherent electromagnetic wave generator, a medium normally absorptively resonant to electromagnetic waves of a predetermined frequency generated by said generator but transmissive bursts of coherent electromagnetic waves wherein the product of the strength of a pulse of said waves and its duration is limited in accordance with the equation where pi 3.1416..., E is the electric field strength of said wave, and t is the duration of said pulse, and further limited such that the duration of said pulse is less than the relaxation time of the response of said medium, means forming two signal paths between said generator and said medium, said signal paths having outputs directed toward an input of said medium so that the outputs of said signal paths cooperate thereat to produce a pulse within the medium which is the sum of the signals traversing said paths, means controlling the level of the signals within said paths so that the pulse area thereof is less than pi so that, whenever both signals are present, a combined signal is produced having a strength greater than pi which then propagates through the medium, and whenever either of said input signals is present alone it is attenuated by the resonant medium and no output pulse is emitted.
 15. In pulse shaping apparatus for modifying electromagnetic waves, means for generating bursts of coherent electromagnetic waves, a medium normally absorptively resonant to electromagnetic waves of a predetermined frequency generated by said last named means but transmissive to bursts thereof characterized by the product of the strength of said burst in its duration being limited in accordance with the equation where pi 3.1416..., E is the electric field strength of said wave, and t is the duration of said pulse, and further in which the burst is limited to a duration less than the relaxation time of the response of said medium, means mounting said generator so that said pulses pass through a predetermined length of said medium, pulses having an area lying between pi and 2 pi being increased in duration and decreased in intensity as they are passed through the medium while pulses having an area lying between 2 pi and 3 pi being increased in intensity and shortened in duration.
 16. Apparatus as in claim 15 further including means for shifting the resonance of the medium so that it becomes transparent to permit the pulse as pi to exist in its modified form in a particular time to appear at the output of the device.
 17. In apparatus for changing the convergence and divergence of electromagnetic waves, means for generating bursts of electromagnetic waves having a predetermined frequency and including means for limiting the product of the strength of said burst in its duration in accordance with the equation where pi 3.1416, E is the electric field strength of said wave, and t is the duration of said pulse, a medium normally resonant to said traveling electromagnetic waves said means for generating said coherent electromagnetic waves further including means for limiting the duration of said pulse to a value less than the relaxation time of the response of said medium and for applying said bursts to said medium so that said waves propagate through the medium, whereby diverging or converging electromagnetic energy within said bursts are collimated by said medium.
 18. In a method for detecting low level electromagnetic signals the steps of providing a medium exhibiting rEsonance response to electromagnetic energy of a predetermined frequency and therefore normally opaque to such electromagnetic waves, forming coherent pulses of electromagnetic waves of said predetermined frequency, limiting the product of the strength of said pulse and its duration to a value in accordance with the equation to slightly less than pi where pi 3.1416..., E is the electric field strength of the applied pulse, and t is the duration of said pulse and further limiting said pulse to a value less than the relaxation time of the response of said medium, applying said pulses to said medium, further applying the low level to be detected to said medium so that said pulse and said low level signal combine to create a pulse within the medium in which the combined pulse satisfies the criteria (where E includes both pulse and signal components) whereby the absence of said low level signal is indicated by the absence of an output pulse from the medium and the presence of said low level signal being sufficient to induce said medium to propagate the combined signal so that the presence of an output pulse from the medium is indicative of the existence of a low level signal applied to the input.
 19. A method as in claim 18 wherein said signals are microwave signals.
 20. Apparatus for investigating the properties of materials comprising a generator for providing an output of coherent electromagnetic waves said generator including means for varying the pulse duration and intensity of the output of said waves as over a range including wherein bursts are formed characterized by a predetermined frequency content and having the property that the product of the strength of said burst and its duration is limited in accordance with the equation where pi 3.1416, E is the electric field strength of said waves and t is the duration of said bursts and further including means for limiting the duration of said bursts to a value less than a predetermined time of an exptected value corresponding to the relaxation time of the material to be investigated so that the bursts are applied thereto, means for detecting the amount remaining of said bursts which have passed through the material.
 21. Apparatus as in claim 20 further including a programmer and computer for controlling and coordinating the apparatus to record the variation in intensity and pulse duration of bursts applied to the sample medium under investigation as a function of the output response from the sample medium.
 22. Apparatus as in claim 20 further including means for sweeping the frequency of the output bursts across a predetermined bandwidth of frequencies.
 23. Apparatus as in claim 20 further including means for varying a thermodynamic variable of the material under investigation so that the changes of the transmission properties of the material can be measured and correlated with the changes in the material due to varying thermodynamic variables.
 24. A method for measuring the bandwidth of a resonance exhibited by a material, said resonance relating to a response to electromagnetic waves so that said material is normally opaque thereto, the steps of forming and applying to said material coherent pulses of said electromagnetic waves each pulse being composed of waves having a frequency content capable of coupling to said resonance response, limiting the product of the strength of said pulse and the duration thereof in accordance with the equation where pi 3.1416, E is the electric field strength of said waves, and t is the duration of said pulse, further limiting the duration of said pulse to a value less than the relaxation time of the response of said medium, subsequently increasing the frequency bandwidth of the input pulses to said material and noting the onset perturbations in the waves transmitted by said medium as the input bandwidth approaches the resonance bandwidtH.
 25. A method for measuring the uniformity of doping of a volume of semiconductor having an impurity therein comprising the steps of measuring the relaxation time of a uniformly doped reference semiconductor sample by applying a coherent traveling electromagnetic wave pulse to said semiconductor sample said pulse being further composed of waves having a frequency count capable of coupling to the resonance of said sample and limiting the product of the strength of said pulse in its duration in accordance with the equation where pi 3.1416, E is the electric field strength of said waves, and t is the duration of said pulse, and further limiting the duration of said pulse to a value less than the relaxation time of the response of said uniformly doped semiconductor, thereafter increasing the duration of said pulse until it is attenuated due to the homogeneous doping of said semiconductor to thereby define a reference relaxation time, applying coherent electromagnetic pulses of energy to successive samples of semiconductor material in which said pulses are also characterized by the equation and a duration slightly less than said reference time, and noting those samples under test which absorbed an input pulse such absorption being indicative of inhomogeneous broadening due to imperfect distribution of the dopants within said sample.
 26. In a method for varying the shape of an electromagnetic wave the steps of passing said wave through a medium exhibiting a resonance to such waves, forming a coherent pulse of said waves having a frequency content capable of coupling to said resonance response of said medium, limiting the product of the strength of the pulse and its duration in accordance with the equation where pi 3.1614, E is the electric field strength of said waves and t is the duration of said pulse limiting the duration of said pulse to a value less than the relaxation time of the response of said medium and applying said pulses to said medium, said medium serving to reform said input pulses into output pulses satisfying the equation
 27. In a method for propagating periodically varying electromagnetic or sound waves through a medium exhibiting a resonance response to such waves and therefore normally opaque to such waves, the steps of forming a coherent pulse of said waves, said pulse being composed of waves having a frequency content capable of coupling to said resonance response, limiting the production of the strength of said pulse and its duration in accordance with the equation where pi 3.1416..., E is the field strength of said waves, and t is the duration of said pulse to a value less than the relaxation time of the response of said medium, and applying one or more of said pulses to said medium. 